Which of the following numbers is a multiple of 3? ${55,75,76,85,89}$
Answer: The multiples of $3$ are $3$ $6$ $9$ $12$ ..... In general, any number that leaves no remainder when divided by $3$ is considered a multiple of $3$ We can start by dividing each of our answer choices by $3$ $55 \div 3 = 18\text{ R }1$ $75 \div 3 = 25$ $76 \div 3 = 25\text{ R }1$ $85 \div 3 = 28\text{ R }1$ $89 \div 3 = 29\text{ R }2$ The only answer choice that leaves no remainder after the division is $75$ $ 25$ $3$ $75$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $3$ are contained within the prime factors of $75$ $75 = 3\times5\times5 3 = 3$ Therefore the only multiple of $3$ out of our choices is $75$. We can say that $75$ is divisible by $3$.